Step-by-Step Algebra Solver
Type an equation and get the full worked solution, line by line, the way a teacher would write it: distribute the minus sign, subtract 5 from both sides, factor the trinomial, square both sides and check for extraneous roots. Handles linear, quadratic (factoring, quadratic formula, completing the square or square roots), higher-degree polynomial, rational, radical, absolute-value, exponential, logarithmic and trigonometric equations; linear, compound, absolute-value and polynomial or rational inequalities with a sign chart and a number line; and systems by substitution, elimination, matrices or Cramer’s rule. Without an equals sign it expands (FOIL), factors (GCF, difference of squares, ac method, grouping) or simplifies rational expressions. Paste plain text or LaTeX; every answer is checked by substitution.
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Results
Notes
- Steps follow textbook rules — inverse operations on both sides, distributing (signs included), the zero-product property, the ac method, the rational root theorem, u-substitution, the log rules, reference angles — and every candidate is substituted back into the original equation; extraneous roots from squaring or from log/denominator restrictions are shown and rejected.
- Inequalities: multiplying or dividing by a negative number reverses the sign; compound inequalities are solved on all three parts at once; polynomial and rational ones use a sign chart. The answer is given in inequality and interval notation, on a number line, and checked with test values.
- log(x) is base 10 unless you choose otherwise; ln(x) is the natural log, log2(x) or log_b(x) any other base. e is Euler’s number and pi is π. Decimals in the input give decimals in the steps.
- Polynomials without rational roots are factored over the rationals where possible; otherwise the real roots are approximated numerically to 10 digits. Equations with no textbook method (like sin x = x/2) fall back to the computer algebra system, or to a numeric root search.
- Systems: two linear equations by substitution or elimination (or the method you pick), larger ones by Gaussian elimination on the augmented matrix or Cramer’s rule; a linear + non-linear pair by substitution. Two-unknown systems are graphed with their crossing points.
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